1. Field of the Invention
The present invention relates generally to consecutive edge modulators, and more specifically, to a consecutive-edge modulator (CEM) having a ternary output and a constant edge-rate.
2. Background of the Invention
Consecutive edge modulators (CEMs) are desirable in applications such as digital-to-analog (D/A) converters and power output circuits due to the effectively doubled control update rate at a given output frequency over that of a traditional pulse width modulator (PWM). Since the pulse output is controlled with respect to both the leading edge and the trailing edge, the control function is more responsive, leading to a lower operating frequency for a given required response.
In particular, in applications requiring a highly stable and accurate output, the CEM output circuit is driven by a noise-shaping modulator that pushes the conversion “noise”, produced due to the discrete nature of the modulator's quantized output, to the high end of the frequency spectrum, where the output filters can effectively remove the noise. Ternary CEMs also provide increased accuracy through improved resolution per quantizer sample, by doubling the possible number of codes per pulse. In some ternary CEM implementations, a pair of CEMs are used to control generation of two streams that either correspond to positive pulses and negative pulses or pulses of the same sign, where the output states correspond to zero, half-maximum and maximum output. For a given quantizer output, the value is divided evenly between the two outputs with any remainder count assigned between the two output streams.
A mismatch shaper typically provides the assignment of the portions of the quantizer output values so that while the assignment of any remainder count is not completely random, the artifacts of the assignment are shaped in the frequency domain so that no undesirable artifacts are generated by the assignment. However, other code-splitting circuits may be used to assign the remainder between the output pulse streams. Any code splitter other than a simple alternating assignment of the remainder count raises the possibility that sequentially adjacent codes will cause a missing transition if non-transitioning codes are permitted for either CEM stream. Simple alternation is generally undesirable, since the attenuation of artifacts introduced by the alternation is low unless the oversampling rate is very high.
A constant edge rate (fixed output frequency) is typically desired for linearity and low distortion from the CEM circuits. Since a pulse is guaranteed to occur within a given window, the rise time and fall time of switching circuits connected to the output of the CEM contributes equally to each pulse period, thereby contributing little or no non-linearity. However, in a ternary CEM (i.e., a CEM that has three distinct output levels), it is possible to have states in which no transition occurs during a particular sample period. In the dual-code ternary system there are possible codes for which there is no transition on one output and other codes for which there is no transition on both outputs. Permitting the range of edge positions to extend to represent either type of non-transitioning code results in distortion and non-linearity in the result of the CEM conversion, when sequentially adjacent samples on one or more of the outputs are at the maximum or minimum value. Existing circuits overcome the above-described problem by constraining the output of the modulator, disallowing those maximum or minimum codes that would result in no transition being generated on one or both of the outputs during a pulse period.
However, such a solution causes loss of substantial dynamic range where the number of overall codes is small. For example, if the total count of the quantizer output of the noise-shaper has 17 levels (−8 to +8), the effective output of the CEM is limited to 13 levels, resulting in a dynamic range that is only approximately 75% of the possible dynamic range. The two quantizer output levels corresponding to full on or full off (−8 and +8) must be disallowed, as either case results in a pulse period with no transition on either output. The quantizer output levels that correspond to only an off count of magnitude 1 (−7 and +7) must also be disallowed, because one of the two outputs will be have no transition during the sample period and if two such codes occur consecutively, a transition will be missed during a sample period. All other values can be supported by the two outputs without having one of the outputs in the off condition for any sample interval, but as noted above, the penalty is loss of substantial potential dynamic range.
Therefore, it would be desirable to provide a noise-shaped PWM method and apparatus that provide operation over a wider dynamic range without generating substantial distortion and/or non-linearity.